--- date: '2024-01-24' description: control system block diagrams with cascade form, parallel form, feedback loops, summing junctions, and transfer function reduction techniques. id: Block Diagrams modified: 2026-06-05 15:08:43 GMT-04:00 seealso: - '[[thoughts/university/twenty-three-twenty-four/sfwr-3dx4/block_diagrams.pdf|sides]]' tags: - sfwr3dx4 title: Block Diagrams created: '2024-01-24' published: '2024-01-24' pageLayout: default slug: thoughts/university/twenty-three-twenty-four/sfwr-3dx4/Block-Diagrams permalink: https://aarnphm.xyz/thoughts/university/twenty-three-twenty-four/sfwr-3dx4/Block-Diagrams.md generator: quartz: v4.6.0 hostedProvider: Cloudflare baseUrl: aarnphm.xyz full: https://aarnphm.xyz/llms-full.txt --- ## Cascade form
"\\usepackage{tikz}\n\\usetikzlibrary{positioning}\n\n\\begin{document}\n\\begin{tikzpicture}[auto, node distance=1.8cm, >=latex]\n\n% Part (a) - Series Block Diagram\n\\node at (2, 1.5) {\\textit{(a)}};\n\n% Nodes for first block diagram\n\\node[] (R) {$R(s)$};\n\\node[draw, rectangle, right=1.5cm of R, minimum width=1.5cm, minimum height=1cm] (G1) {$G_1(s)$};\n\\node[draw, rectangle, right=1.5cm of G1, minimum width=1.5cm, minimum height=1cm] (G2) {$G_2(s)$};\n\\node[draw, rectangle, right=1.5cm of G2, minimum width=1.5cm, minimum height=1cm] (G3) {$G_3(s)$};\n\\node[right=1.5cm of G3] (C) {$C(s)$};\n\n% Arrows for first block diagram\n\\draw[->] (R) -- (G1);\n\\draw[->] (G1) -- (G2);\n\\draw[->] (G2) -- (G3);\n\\draw[->] (G3) -- (C);\n\n% Part (b) - Simplified Block Diagram\n\\node at (2, -1.5) {\\textit{(b)}};\n\n% Nodes for simplified block diagram\n\\node[] (R2) at (0, -3) {$R(s)$};\n\\node[draw, rectangle, right=3.5cm of R2, minimum width=3.5cm, minimum height=1cm] (G123) {$G_3(s)G_2(s)G_1(s)$};\n\\node[right=2cm of G123] (C2) {$C(s)$};\n\n% Arrows for simplified block diagram\n\\draw[->] (R2) -- (G123);\n\\draw[->] (G123) -- (C2);\n\n\\end{tikzpicture}\n\\end{document}"tikz diagram
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## Parallel form
"\\usepackage{tikz}\n\\usetikzlibrary{positioning, arrows.meta}\n\n\\begin{document}\n\\begin{tikzpicture}[auto, node distance=1.5cm, >=Latex]\n\n% -------------------- PART (a) --------------------\n\\node at (1.5, 1.5) {\\textit{(a)}};\n\n% Input node\n\\node (R) at (1.5, -1.5) {$R(s)$};\n\n% Blocks G1, G2, G3\n\\node[draw, rectangle, minimum width=1.5cm, minimum height=1cm, right=1.5cm of R, yshift=1.5cm] (G1) {$G_1(s)$};\n\\node[draw, rectangle, minimum width=1.5cm, minimum height=1cm, right=1.5cm of R] (G2) {$G_2(s)$};\n\\node[draw, rectangle, minimum width=1.5cm, minimum height=1cm, right=1.5cm of R, yshift=-1.5cm] (G3) {$G_3(s)$};\n\n% Summing point\n\\node[draw, circle, minimum size=0.5cm, right=4.5cm of R] (sum) {\\Large $\\Sigma$};\n\n% Output node\n\\node[right=1.5cm of sum] (C) {$C(s)$};\n\n% Arrows from R to blocks\n\\draw[->] (R) -- (G1);\n\\draw[->] (R) -- (G2);\n\\draw[->] (R) -- (G3);\n\n% Arrows from blocks to summing point\n\\draw[->] (G1.east) -- ++(2,0) |- (sum.north);\n\\draw[->] (G2.east) -- ++(0.5,0) -- (sum.west);\n\\draw[->] (G3.east) -- ++(2,0) |- (sum.south);\n\n% Arrow from summing point to output\n\\draw[->] (sum.east) -- (C);\n\n% -------------------- PART (b) --------------------\n\\node at (1.5, -5) {\\textit{(b)}};\n\n% Simplified block diagram\n\\node[draw, rectangle, minimum width=3.5cm, minimum height=1cm, below=4cm of R] (simplified) {$\\pm G_1(s) \\pm G_2(s) \\pm G_3(s)$};\n\n% Input and output for simplified block\n\\node[left=1.5cm of simplified] (R2) {$R(s)$};\n\\node[right=1.5cm of simplified] (C2) {$C(s)$};\n\n% Arrows for simplified block\n\\draw[->] (R2) -- (simplified);\n\\draw[->] (simplified) -- (C2);\n\n\\end{tikzpicture}\n\\end{document}"tikz diagram
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## Feedback loop ![[thoughts/university/twenty-four-twenty-five/sfwr-4aa4/feedback-loop-transfer-function.webp]] ## Moving through summing junction ![[thoughts/university/twenty-three-twenty-four/sfwr-3dx4/images/summing junction.webp]] ## Reduction via Familiar Forms